Theorems · Theorem · commutative algebra
Algebra.fg_trans
∀ {R : Type u} {A : Type v} [inst : CommSemiring R] [inst_1 : CommSemiring A] [inst_2 : Algebra R A] {s t : Set A},
(Subalgebra.toSubmodule (Algebra.adjoin R s)).FG →
(Subalgebra.toSubmodule (Algebra.adjoin (↥(Algebra.adjoin R s)) t)).FG →
(Subalgebra.toSubmodule (Algebra.adjoin R (s ∪ t))).FG- Defined in
- Mathlib.RingTheory.Adjoin.FG
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites37
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Moduleproof · cited by 20,661
- Semiringproof · cited by 13,802
- AddCommMonoidproof · cited by 12,281
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Submodulestatement and proof · cited by 7,192
- Finsuppproof · cited by 5,255
- le_antisymmproof · cited by 2,068
- Set.Finiteproof · cited by 1,814
- Submodule.spanproof · cited by 1,504
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.